Pythagorean Theorem/Transcript
Transcript Title text reads, The Mysteries of Life with Tim and Moby. Moby is measuring wood for a construction project. He cuts a piece with a saw, but it's too short. He beeps. Tim looks on. TIM: Measure twice; cut once. Moby beeps. A letter appears. Text reads as Tim narrates: Dear Tim and Moby, Can you explain the Pythagorean theorem? From, Carrie. TIM: Sure thing. The Pythagorean theorem applies to right triangles like this one. On-screen, Tim holds up a wooden triangle. TIM: Every right triangle has a right angle. That’s any angle that measures exactly 90 degrees. The side opposite that right angle is the hypotenuse, and the sides adjacent to that right angle are called the legs. Labels appear on the sides of the wooden triangle, reading: hypotenuse, leg, and leg. Moby writes measurements for each side: the hypotenuse is 5 centimeters, and the legs are 3 centimeters and 4 centimeters. TIM: The Pythagorean theorem says that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. An equation appears, reading, c squared equals a, squared plus b squared. Moby beeps. TIM: Yes, it’s named after the Greek mathematician Pythagoras, who is often credited with coming up with the equation. In truth, it was probably known to mathematicians before him, at least in part. But Pythagoras got the credit for some reason, so here we are! Moby beeps. TIM: Okay, let’s try it out! On-screen, the labels for hypotenuse, leg, and leg are replaced by c, a, and b. TIM: C, is our hypotenuse. We can plug in 5 for that, and we know that 5 squared is 25. Leg a, measures 4 centimeters, so a, squared is 16. And b, is 3 centimeters, which makes b squared 9. On-screen, the equation, c squared equals a, squared plus b squared becomes, 25 equals 16 plus 9. TIM: 16 plus 9 is equal to 25. We just proved the Pythagorean theorem. Moby beeps. He holds up another wooden triangle. The hypotenuse is labeled 10, and one of the legs is labeled 6. TIM: We can use the Pythagorean theorem to find the length of a triangle’s leg, as long as we know the lengths of the other leg and the hypotenuse. On-screen, the equation, c squared equals a, squared plus b squared becomes, 10 squared equals 6 squared plus b squared. TIM: 10 squared is 100, and 6 squared is 36. On-screen, the equation becomes, 100 equals 36 plus b squared. TIM: We subtract 36 from each side, which gives us, 64 equals b squared. On-screen, the equation becomes, 64 equals b squared. TIM: B, equals the square root of 64, which is 8. So leg b, is 8 centimeters long. Pretty cool that the Pythagorean theorem works, eh, Moby? Moby? On-screen, Tim hears sawing and hammering sounds. Moby beeps. He stands in front of a mountain of toothpicks. TIM: Wow, look at all those toothpicks you made. You know they sell those in stores, right? Moby beeps. TIM: That's true. These are made of nicer wood. Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts